$86$ people attended a baseball game. Everyone there was a fan of either the home team or the away team. The number of home team fans was $46$ less than $2$ times the number of away team fans. How many home team and away team fans attended the game?
Answer: Let $x$ equal the number of home team fans and $y$ equal the number of away team fans. The system of equations is then: ${x+y = 86}$ ${x = 2y-46}$ Solve for $x$ and $y$ using substitution. Since $x$ has already been solved for, substitute ${2y-46}$ for $x$ in the first equation. ${(2y-46)}{+ y = 86}$ Simplify and solve for $y$ $ 2y-46 + y = 86 $ $ 3y-46 = 86 $ $ 3y = 132 $ $ y = \dfrac{132}{3} $ ${y = 44}$ Now that you know ${y = 44}$ , plug it back into ${x = 2y-46}$ to find $x$ ${x = 2}{(44)}{ - 46}$ $x = 88 - 46$ ${x = 42}$ You can also plug ${y = 44}$ into ${x+y = 86}$ and get the same answer for $x$ ${x + }{(44)}{= 86}$ ${x = 42}$ There were $42$ home team fans and $44$ away team fans.